confidence game

Also,
confidence trick;
con game. A swindle in which the victim is defrauded after his or her trust has been won. For example, The police warned of a confidence game in which people were asked to turn over valuables for a so-called appraisal, or The typical confidence trick is easy to spot if you know what to look for, or I almost let myself be taken in by her con game—she seemed so sincere. These terms, which use confidence in the sense of “trust,” date from the mid-1800s. They also gave rise to confidence man (or con man) for the swindler.

con game

any elaborate swindling operation in which advantage is taken of the confidence the victim reposes in the swindler. Some countries have created a statutory offense of this name, though the elements of the crime have never been clearly defined by legislation, and the scope of proscribed behaviour remains subject to varying interpretations among jurisdictions.